Bulletin of the American Mathematical Society

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Authors: J. F. Berglund, H. D. Junghenn and P. Milnes
Title: Compact right topological semigroups and generalizations of almost periodicity
Additional book information: Lecture Notes in Math., vol. 663, Springer-Verlag, Berlin-Heidelberg-New York, 1978, x + 243 pp., $12.00.

Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848. MR 45941, DOI 10.1090/S0002-9939-1951-0045941-1

J. F. Berglund and K. H. Hofmann, Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Mathematics, No. 42, Springer-Verlag, Berlin-New York, 1967. MR 0223483

S. Bochner, Beiträge zur Theorie der fastperiodischen Funktionen, Math. Ann. 96 (1927), no. 1, 119–147 (German). MR 1512308, DOI 10.1007/BF01209156

S. Bochner, Abstrakte Fastperiodische Funktionen, Acta Math. 61 (1933), no. 1, 149–184 (German). MR 1555374, DOI 10.1007/BF02547790

S. Bochner and J. von Neumann, Almost periodic functions in groups. II, Trans. Amer. Math. Soc. 37 (1935), no. 1, 21–50. MR 1501777, DOI 10.1090/S0002-9947-1935-1501777-9

H. Bohr, Fastperiodische Funktionen, Springer-Verlag, Berlin-New York, 1974 (German). Reprint. MR 0344794

Mahlon M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544. MR 92128

Mahlon M. Day, Fixed-point theorems for compact convex sets, Illinois J. Math. 5 (1961), 585–590. MR 138100

Mahlon Marsh Day, Correction to my paper “Fixed-point theorems for compact convex sets”, Illinois J. Math. 8 (1964), 713. MR 169210

Karl W. Folley (ed.), Semigroups, Academic Press, New York-London, 1969. MR 0258992

K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63–97. MR 131784, DOI 10.1007/BF02559535

W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217–240. MR 36455, DOI 10.1090/S0002-9947-1949-0036455-9

E. Granirer, Extremely amenable semigroups, Math. Scand. 17 (1965), 177–197. MR 197595, DOI 10.7146/math.scand.a-10772

Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549

Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915

Karl Heinrich Hofmann and Paul S. Mostert, Elements of compact semigroups, Charles E. Merrill Books, Inc., Columbus, Ohio, 1966. MR 0209387

Konrad Jacobs, Neuere Methoden und Ergebnisse der Ergodentheorie, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 29, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0123676

E. R. van Kampen, Locally bicompact abelian groups and their character groups, Ann. of Math. (2) 36 (1935), no. 2, 448–463. MR 1503234, DOI 10.2307/1968582

Anthomy ToMing Lau, Invariant means on almost periodic functions and fixed point properties, Rocky Mountain J. Math. 3 (1973), 69–76. MR 324313, DOI 10.1216/RMJ-1973-3-1-69

W. Maak, Fastperiodische Funktionen, Die Grundlehren der mathematischen Wissenschaften, Band 61, Springer-Verlag, Berlin-New York, 1967 (German). Zweite, korrigierte Auflage. MR 0215015

Theodore Mitchell, Fixed points and multiplicative left invariant means, Trans. Amer. Math. Soc. 122 (1966), 195–202. MR 190249, DOI 10.1090/S0002-9947-1966-0190249-2

Theodore Mitchell, Topological semigroups and fixed points, Illinois J. Math. 14 (1970), 630–641. MR 270356

J. von Neumann [1929], Zur allgemeine Theorie des Masses, Fund. Math. 13, 73-116.

J. v. Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445–492. MR 1501752, DOI 10.1090/S0002-9947-1934-1501752-3

T. Tannaka [1939], Uber den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tôhoku Math. J. 45, 2-12.

B. L. van der Waerden, Stetigkeitssätze für halbeinfache Liesche Gruppen, Math. Z. 36 (1933), no. 1, 780–786 (German). MR 1545369, DOI 10.1007/BF01188647

R. Arens [1951], The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2, 839-848. MR 0045941




J. F. Berglund and K. H. Hoffmann [1967], Compact semitopological semigroups and weakly almost periodic functions. Lecture Notes in Math., vol. 42, Springer-Verlag, Berlin and Heidelberg, New York. MR 223483




S. Bochner [1927], Beiträge zur Theorie der fastperiodische Funktionen. I, II. Math. Ana 96, 119-147; 383-409. MR 1512308




S. Bochner, [1933], Abstrakte fastperiodische Funktionen, Acta Math. 61, 149-184. MR 1555374




S. Bochner and J. von Neumann [1935], Almost periodic functions in groups, Trans. Amer. Math. Soc. 37, 21-50. MR 1501777




H. Bohr [1932], Fastperiodische Funktionen, Verlag von Julius Springer, Berlin. MR 344794




M. M. Day [1957], Amenable semigroups, Illinois J. Math. 1, 509-544. MR 92128




M. M. Day [1961], Fixed point theorems for compact convex sets, Illinois J. Math. 5, 585-590. MR 138100




M. M. Day [1964], Correction to fixed point theorems for compact convex sets, Illinois J. Math. 8, p. 713. MR 169210




M. M. Day [1969], Semigroups and amenability. Semigroups, edited by K. W. Folley, Academic Press, New York and London, pp. 5-52. MR 258992




K. de Leeuw and I. Glicksberg [1961], Applications of almost periodic compactifications, Acta Math. 105, 63-97. MR 131784




W. F. Eberlein [1949], Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67, 217-240. MR 36455




E. Granirer [1965], [1967], Extremely amenable semigroups. I, II, Math. Scand. 17, 177-197; 20, 93-113. MR 197595




F. P. Greenleaf [1969], Invariant means on topological groups and their applications, van Nostrand, New York. MR 251549




E. Hewitt and K. A. Ross [1963], Abstract harmonic analysis, Springer-Verlag, Berlin-Göttingen-Heidelberg. MR 156915




K. H. Hoffmann and P. S. Mostert [1966], Elements of compact semigroups, Charles E. Merrill, Columbus, Ohio. MR 209387




K. Jacobs [1960], Neuere Methoden und Ergebnisse der Ergodentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg. MR 123676




E. R. van Kampen [1935], Locally bicompact abelian groups and their character groups, Ann. of Math. (2) 36, 448-463. MR 1503234




A. T. Lau [1973], Invariant means on almost periodic functions and fixed point properties, Rocky Mountain J. Math. 3, 69-76. MR 324313




W. Maak [1967], Fastperiodische Funktionen, Springer-Verlag, Berlin and Heidelberg, New York. MR 215015




T. Mitchell [1966], Fixed points and multiplicative left invariant means, Trans. Amer. Math. Soc 122, 195-202. MR 190249




T. Mitchell [1970], Topological semigroups and fixed points, Illinois J. Math. 14, 630-641. MR 270356




J. von Neumann [1929], Zur allgemeine Theorie des Masses, Fund. Math. 13, 73-116.




J. von Neumann (1934), Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36, 445-492. MR 1501752




T. Tannaka [1939], Uber den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tôhoku Math. J. 45, 2-12.




B. L. van der Waerden [1933], Stetigkeitssatze der halbeinfachen Lieschen Gruppen, Math. Z. 36, 780-786. MR 1545369